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<h3 class="heading"><span class="type">Paragraph</span></h3>
<p><dfn class="terminology">Solution</dfn> Seek a solution of the form <span class="process-math">\(y=e^{r x}\)</span> and substitute it into the ODE, one has</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
r^2+2 r+2=0.
\end{equation*}
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<p class="continuation">The complex conjugate roots are</p>
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\begin{equation*}
r_1=\frac{-2+\sqrt{4-4 \cdot 2}}{2}=-1+i,\quad r_2=-1-i.
\end{equation*}
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<p class="continuation">The general solution is</p>
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\begin{equation*}
y=C_1 e^{\lambda x} \cos \mu x+C_2 e^{\lambda x} \sin \mu x=C_1  e^{- x} \cos x+C_2 e^{- x} \sin  x.
\end{equation*}
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